Question

[Nguyễn Ngọc Minh]

3/4 x 8/9 x 15/16 x ......... x 99/100

Answer 1

[Vũ Cao Minh⁀ᶦᵈᵒᶫ ( ✎﹏IDΣΛ亗 )]

\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{99}{100}\)

\(=\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times...\times\frac{9\times11}{10\times10}\)

\(=\frac{\left(1\times3\right)\times\left(2\times4\right)\times\left(3\times5\right)\times...\times\left(9\times11\right)}{\left(2\times2\right)\times\left(3\times3\right)\times\left(4\times4\right)\times...\times\left(10\times10\right)}\)

\(=\frac{1\times2\times3\times...\times9\times3\times4\times5\times...\times11}{2\times3\times4\times...\times10\times2\times3\times4\times...\times10}\)

\(=\frac{1\times11}{10\times2}=\frac{11}{20}\)